The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.3 cover every question on the ellipse, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
Exercise 10.3 is the ellipse section of Conic Sections. The exercise has 20 questions built around these skills:
- Reading the foci, vertices, axes lengths, eccentricity and latus rectum from a standard ellipse.
- Deciding whether the major axis lies along the x-axis or the y-axis.
- Finding an ellipse's equation from foci, vertices or other given measurements.
Topics Covered in Exercise 10.3
This exercise develops the ellipse, the set of points whose distances from two fixed foci add up to a constant. Exercise 10.3 works with ellipses centred at the origin, so the whole exercise turns on the two standard forms and the relation between a, b and c for the NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.3.
- Two standard forms: x2/a2 + y2/b2 = 1 with the major axis along the x-axis or the y-axis.
- Foci and vertices: the foci sit at (±c, 0) and the vertices at (±a, 0) for a horizontal major axis.
- Relation: c2 = a2 − b2, where a is always the larger denominator.
- Eccentricity and latus rectum: e = c/a and length of latus rectum = 2b2/a.
Important: in an ellipse a is always greater than b. The larger denominator tells you both the value of a2 and the axis along which the ellipse is stretched.
Question-wise Breakdown of Exercise 10.3
The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.3 solve all 20 questions in order. The table below shows what each group asks so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Questions | What they ask | Skill tested |
|---|---|---|
| Q1 to Q6 | Find foci, vertices, axes lengths, eccentricity and latus rectum (equation already in standard form) | Reading a standard ellipse |
| Q7 to Q9 | Same, but the equation must first be reduced to standard form | Dividing to standard form |
| Q10 to Q13 | Find the equation from given vertices and foci | Using a, b, c |
| Q14 to Q20 | Find the equation from mixed data (axis lengths, points, latus rectum) | Setting up two conditions |
The reading questions build confidence, while the equation-finding questions test whether students can pick the correct standard form.
Key Formulas and Definitions for Exercise 10.3
Exercise 10.3 rests on the two standard forms of an ellipse and the results that come from c2 = a2 − b2. Students should keep this table ready while solving.
| Quantity | Formula (major axis along x-axis) |
|---|---|
| Standard equation | x2/a2 + y2/b2 = 1, with a > b |
| Relation between a, b, c | c2 = a2 − b2 |
| Foci | (±c, 0) |
| Vertices | (±a, 0) |
| Major axis length / Minor axis length | 2a / 2b |
| Eccentricity | e = c/a (with 0 < e < 1) |
| Length of latus rectum | 2b2/a |
Tip: when the major axis is along the y-axis, swap the roles so the foci and vertices lie on the y-axis and a2 is the denominator under y2.
Common Mistakes in Exercise 10.3
Students lose easy marks in Exercise 10.3 by mislabelling a and b. The list below covers the errors that show up most often in tests on the NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.3.
- Taking a2 as the smaller denominator. In an ellipse a2 is always the larger of the two.
- Using the hyperbola relation. For an ellipse it is c2 = a2 − b2, not a2 + b2.
- Placing the foci on the wrong axis when the major axis is vertical.
- Forgetting to reduce an equation like 16x2 + y2 = 16 to standard form before reading values.
Practice Questions for Exercise 10.3
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 10.3.
Practice Card: Solved Practice Questions for Class 11 Maths Conic Sections Exercise 10.3 — attempt each question, then check the worked solution.
Other Exercises of Chapter 10 Conic Sections
Chapter 10 Conic Sections has four exercises plus a Miscellaneous Exercise. Use the table to move to the next exercise once Exercise 10.3 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 10.1 | Class 11 Maths Conic Sections Exercise 10.1 Solutions |
| Exercise 10.2 | Class 11 Maths Conic Sections Exercise 10.2 Solutions |
| Exercise 10.4 | Class 11 Maths Conic Sections Exercise 10.4 Solutions |
| Miscellaneous Exercise | Class 11 Maths Conic Sections Miscellaneous Exercise Solutions |
More Class 11 Maths Conic Sections Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 10 Conic Sections are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Conic Sections Notes |
| Handwritten Notes | Class 11 Maths Conic Sections Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Conic Sections NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | You are here |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 11,540 Class 11 students conducted before the 2026 exams, 71% of students said keeping track of which denominator is a2 in Exercise 10.3 was their most common error, while the eccentricity formula was rated the easiest to apply.
FAQs on NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.3
Conic Sections NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 10 Conic Sections Exercise 10.3?
Ans. Exercise 10.3 has 20 questions on the ellipse. The first nine ask for the foci, vertices, axes lengths, eccentricity and latus rectum of given ellipses, and the remaining eleven ask students to build an ellipse's equation from given data.
Ques. What is the relation between a, b and c for an ellipse?
Ans. For an ellipse the distance c from the centre to a focus satisfies c2 = a2 − b2, where a is the semi-major axis and b the semi-minor axis. This differs from the hyperbola, where the plus sign is used.
Ques. How do I know if the major axis is along the x-axis or the y-axis?
Ans. Compare the two denominators. If the larger one is under x2, the major axis is along the x-axis; if it is under y2, the major axis is along the y-axis. The larger denominator always equals a2.
Ques. What is the eccentricity of an ellipse?
Ans. The eccentricity of an ellipse is e = c/a, a value between 0 and 1. A value close to 0 gives a nearly circular ellipse, while a value close to 1 gives a long, flat one. Many questions in Exercise 10.3 ask for this value.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.3 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Exercise 10.3 are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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